Backward stochastic differential equations and partial differential equations with quadratic growth

Abstract

We provide existence, comparison and stability results for one-dimensional backward stochastic differential equations (BSDEs) when the coefficient (or generator) F(t, Y, Z) is continuous and has a quadratic growth in Z and the terminal condition is bounded. We also give, in this framework, the links between the solutions of BSDEs set on a diffusion and viscosity or Sobolev solutions of the corresponding semilinear partial differential equations.